Physical unclonable functions (PUFs) have emerged as a favorable hardware security primitive, they exploit the process variations to provide unique signatures. CMOS-based PUFs are the most popular type, however, most existing CMOS PUFs are found to be vulnerable to modeling attacks. Memristors leveraging nanotechnology fabrication processes and highly nonlinear behavior became an interesting alternative to the existing CMOS-based PUF technology. Memristor-based PUFs are emerging due to the inherent randomness at both the memristor level due to the cycle-to-cycle (C2C) programming variation of the device. Our study focuses on building a machine learning (ML) analysis and attack framework of tools on Cu/HfO2-x/p++Si memristor-based PUF (MR-PUF). Our objective is to test the resiliency of the security margins of the presented PUF using ML analysis tools. Our main contribution is a holistic study that focuses on attacking the randomness output resiliency based on building randomness predictors using Logistic Regression (LR), Support Vector Machine (SVM), Gaussian Mixture Models (GMM), K-means, K-means++, Random Forest, XGBoost and LSTM, within efficient time, and data complexity. Our results yield low accuracy and ROC results of within 0.49-0.52 and 0.49-0.52 respectively, indicating failure in predicting random data demonstrates efficient randomness prediction resiliency of the MR-PUF. The efficient time and data complexities of these attacks illustrated in this study are yielded to be linear and quadratic resulting in attack execution time in seconds and 5032 training samples combined with 2157 testing samples to verify the randomness of PUF.